134 (2017) 649e658

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The economics of from currents

* Binghui Li a, , Anderson Rodrigo de Queiroz a, Joseph F. DeCarolis a, John Bane b, Ruoying He c, Andrew G. Keeler d, Vincent S. Neary e a Department of Civil, Construction, & Environmental Engineering, North Carolina State University, Raleigh, NC, 27695-7908, United States b Department of Marine Sciences, University of North Carolina, Chapel Hill, NC, 27599-3300, United States c Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, NC, 27695-7908, United States d UNC Coastal Studies Institute, Wanchese, NC, 27981, United States e Water Power Technologies Department, Sandia National Laboratory, Albuquerque, NM, 87123, United States article info abstract

Article history: Hydrokinetic turbines harnessing energy from ocean currents represent a potential low carbon electricity Received 6 January 2017 source. This study provides a detailed techno-economic assessment of ocean turbines operating in the Received in revised form Gulf Stream off the North Carolina coast. Using hindcast data from a high-resolution ocean circulation 27 May 2017 model in conjunction with the US Department of Energy's reference model 4 (RM4) for ocean turbines, Accepted 9 June 2017 we examine resource quality and apply portfolio optimization to identify the best candidate sites for Available online 9 June 2017 ocean turbine deployment. We find that the lowest average levelized cost of electricity (LCOE) from a single site can reach 400 $/MWh. By optimally selecting geographically dispersed sites and taking Keywords: energy advantage of economies of scale, the variations in total energy output can be reduced by an order of Gulf Stream magnitude while keeping the LCOE below 300 $/MWh. Power take-off and transmission infrastructure Portfolio optimization are the largest cost drivers, and variation in resource quality can have a significant influence on the Energy economics project LCOE. While this study focuses on a limited spatial domain, it provides a framework to assess the Renewable generation techno-economic feasibility of ocean current energy in other western boundary currents. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction electricity generation, especially the Gulf Stream [5e7,10e12], the Kuroshio Current [13,14], and the Agulhas Current [15e17]. These resources, which include ocean waves, tides, are all jet-like oceanic western boundary currents, which are open ocean currents as well as gradients in ocean temperature [1] among the swiftest large-scale marine currents. Their current and salinity [2], could serve as an important low carbon renewable speeds are fast enough to be considered excellent energy resources energy source. Previous research has shown great potential for [11,18]. These western boundary currents typically are thousands of marine electricity generation worldwide [3e9]. The available ki- km in length, about 100 km wide, extend to at least 1000 m depth, netic energy in US coastal waters associated with wave, tidal, and and have the strongest current speed at the surface near the center ocean current energy resources is estimated to be 1170 TWh/yr [8], of the current [11]. 222e334 TWh/yr [9] and 45e163 TWhyr [7], respectively. As the most intensely studied ocean current, the Gulf Stream Ocean currents (i.e., non-tidal marine currents) are seawater begins in the Caribbean and terminates in the North Atlantic Ocean. circulations driven by a combination of wind, density, and pressure This fast moving ocean current brings a significant amount of heat differences in the ocean [1]. Ocean currents mostly flow horizon- and salt to the European continent, and also provides an opportu- tally and typically have their highest flow velocities near the sur- nity for energy capture. In the US, the most plausible locations to face. On average, they will have a prevailing direction, but temporal harness Gulf Stream energy are in the Florida Straits and off the variability can at times be strong. Ocean currents have been studied North Carolina coast, the two locations where the current makes its over the past several decades as a potential energy source for closest approach to shore. The estimated extractable energy from the Florida Current (i.e., the portion of the Gulf Stream within the Florida Straits) ranges from 1 GW to 10 GW [5e7], and the portion of the Gulf Stream within 200 miles of the US coastline between * Corresponding author. Florida and North Carolina can yield approximately 9 GW or E-mail address: [email protected] (B. Li). http://dx.doi.org/10.1016/j.energy.2017.06.048 0360-5442/© 2017 Elsevier Ltd. All rights reserved. 650 B. Li et al. / Energy 134 (2017) 649e658

80 TWh per year of electrical power [7]. tracer (temperature and salinity) advections were solved with a Most ocean currents exhibit some degree of path meandering third-order upstream scheme in the horizontal direction and a [19e25] as well as periods of acceleration and deceleration. As a fourth-order centered scheme in the vertical direction. The hori- consequence, the ocean current velocity at a specific location is zontal mixing for both the momentum and tracer utilized the subject to temporal variability [26]. Previous studies [19,23,24,27] harmonic formulation with 100 and 20 m2/s as the momentum and have shown that the lateral movements of the Gulf Stream from tracer mixing coefficient, respectively. Turbulent mixing for both the Florida Straits to Cape Hatteras, NC can be significant due to momentum and tracers was computed using the Mellor/Yamada wind forcing, flow instabilities, and bathymetric effects. Along the Level-2.5 closure scheme [39]. For open boundary conditions, the southeastern US coast, the standard deviation of the lateral Gulf model was nested inside the 1/12 global data assimilative HYCOM/ Stream position displacement increases from 5 to 10 km within the NCODA [40] output superimposed with the 6 major tidal constit- Florida Straits to an approximate 40 km local maximum down- uent forcing derived from an ADCIRC tidal model [41] simulation of stream of a bottom topographic feature off Charleston, SC known as the western Atlantic. the "Charleston Bump" (31e32 N latitude). The standard devia- The MABSAB sub-domain selected for analysis was 77 Wto74 tion in the Stream's lateral displacement decreases moving north- W, 33 Nto36 N, which includes the strongest, near-shore Gulf eastward (downstream) from the Bump, to approximately Stream current off the North Carolina coast. While the fastest Gulf 10e20 km at Cape Hatteras, NC. These path variations will influence Stream currents are closest to the surface, we assume the turbines the cost-effectiveness of Gulf Stream energy extraction. are installed at a depth of approximately 50 m below the sea sur- Previous work includes technical assessments of marine turbine face to accommodate the drafts of large ships and to keep turbine design and performance, mostly to address tidal energy applica- hardware out of the surface wave zone. The study domain is shown tions [28e35]. In addition, a detailed cost analysis for a hypothetical in Fig. 1: the 334 km 280 km rectangle is discretized into a project in the Florida Straits has been performed [10,36]. However, 2km 2 km mesh grid with 19,188 grid points. Daily average the Florida Current is confined within the Florida Straits, which is current speeds for the years 2009e2014 are used in this study approximately 100 km wide between the Florida peninsula and the [38,42,43]. Bahama Banks. By contrast, significant meanders are observed for The electricity output of the turbine at a given current velocity is the Gulf Stream off the North Carolina coast [11,19]. While resource expressed by the following equation: assessments conducted at several discrete locations near Cape Hatteras, NC indicate potential for commercial development 1 PðvÞ¼ hC rAv3 (1) [11,37], they do not tie ocean current resource estimates to the 2 p economic performance of turbine arrays. This paper represents a significant extension of existing work by where v is the current velocity, A is the swept rotor area, r is the providing a comprehensive techno-economic assessment of ocean density of sea water, Cp is the power coefficient that accounts for current energy off the North Carolina coast. Our analysis is the first the conversion of current power to mechanical power, and h is the to combine a multi-year resource assessment based on output from combined power chain conversion efficiency, which includes the a high-resolution ocean circulation model, a portfolio optimization gearbox, generator, and power inverter efficiencies to identify optimal locations to install turbine arrays, and a lev- (see Supplementary Table F for values of the parameters). The elized cost analysis that considers the tradeoff between resource design and performance of the ocean current turbine is adopted quality and distance to shore. Furthermore, this paper represents from Neary et al. [10]. The design represents a moored glider with the first application of portfolio optimization in order to identify a four axial flow marine turbines. The rated capacity of each turbine diverse set of generation sites that hedge against the risk of future is 1 MW, and the total capacity of each unit is 4 MW. The power Gulf Stream meanders. The structure is as follows. Section 2 de- curve is adapted from Neary et al. [10] but adjusted for the lower scribes the model assumptions used for resource assessment and the techno-economic study, and introduces the portfolio optimi- zation model. The results are presented in Section 3, and Section 4 describes the insights and conclusions from this study.

2. Methods

2.1. Resource characterization

Gulf Stream resource data is obtained from a realistic high- resolution regional ocean circulation model, which is used to hindcast the circulation of the Middle Atlantic Bight (MAB), South Atlantic Bight (SAB) and parts of Gulf Stream, Slope Sea, and Sar- gasso Sea [38]. The MABSAB model is based on the Regional Ocean Modeling System (ROMS), a free-surface, terrain-following, primi- tive equations ocean model in widespread use for estuarine, coastal, and regional ocean-wide applications [38]. The MABSAB model covers the domain from 81.89 W to 69.80 W, 28.41 Nto 41.84 N. The horizontal resolution is approximately 2 km. Depth is represented by 36 terrain-following layers [38]. Model bathymetry was interpolated from National Geophysical Data Center (NGDC) 2-Minute Gridded Global Relief Data. Mo- mentum advection equations were solved using a third order up- Fig. 1. The study domain near the North Carolina coast, as represented by a dashed stream bias scheme for three-dimensional velocity and a fourth- box. The assumed grid tie-in point is located at Morehead City, NC, which is marked order centered scheme for two-dimensional transport, whereas with a circle. Isobaths are shown in meters. B. Li et al. / Energy 134 (2017) 649e658 651 average current velocity encountered off the North Carolina coast technologies based on the net present value of different portfolios (Supplementary Figure C). Similar to a wind turbine, the maximum [52]. To our knowledge, our work is the first attempt to apply MVP electricity production of each turbine is limited by the installed to identify optimal allocation of hydrokinetic turbines. generator capacity. We also assume that the space between In our study, the installed turbine capacity is optimally distrib- neighboring units is 1 km, and for simplicity, the wake from up- uted across sites (i.e., grid cells) within the study domain to form a stream units does not affect the performance of downstream units portfolio. We wish to achieve a pre-determined system target ca- [10]. Given this configuration, the average installed capacity in a pacity factor e analogous to the expected return e while mini- single 2 km 2 km grid cell is 16 MW. See Supplementary Fig. B for mizing total variance in aggregate output, which serves as a a detailed layout of generation units. measure of system risk. In addition, we add the following con- fi ð ; Þ The site-speci c annual electricity production (Eij) at grid i j is straints: (1) the number of turbine units installed in a single grid obtained by integrating the product of the turbine's output at a cell must be an integer and cannot exceed a maximum of four units specific current velocity, PðvÞ, with the velocity probability density, per cell or 16 MW, (2) the investor may limit the number of selected ðvÞ fi Pr ij, over the entire velocity interval: grid cells within an appropriate range, and (3) the investor may x the total installed capacity of the project. In addition, the anchoring Zvmax system limits the seabed depth [53], so we assume that the turbines ¼ $h $ ðvÞ$ ðvÞ v Eij AF TL 8760 P Pr ijd (2) can only be installed where the seabed depth is between 100 m and 0 2500 m. With all the information above, we construct a 2-stage optimi- h where, AF is the annual availability factor and TL is the trans- zation model (see Supplementary Notes 1 for the model formula- mission line efficiency. A discretized probability distribution was tion). We assume that a marine current installation with a total obtained by binning the daily average velocities from the MABSAB capacity of 80 MW will be deployed across a maximum of 5 sites, model over the entire 6-year period into a set of velocity ranges. with the installed capacity within each site less than or equal to The velocity probability distribution is provided in Supplementary 16 MW. This scenario represents a plausible utility scale deploy- Fig. C, along with the assumed power curve. ment of generating units. The implementation of the 2-stage model The estimated annual electricity production is used to calculate is developed using MATLAB and CPLEX on a workstation with 24 the corresponding site-specific capacity factors. The capacity factor cores and 256 GB of memory. (CF) at each site is defined as the ratio of its estimated annual electricity production to its maximum annual electricity produc- 2.3. Economic assumptions tion, if it operated continuously at its full capacity. A higher site- specific capacity factor implies higher electricity production given Costs associated with Gulf Stream project development draw the same amount of installed capacity. heavily on the RM4 marine turbine design detailed in Neary et al. [10]. The design of the RM4 marine turbine involved rigorous 2.2. Portfolio optimization procedure analysis, including the specification of individual parts associated with subcomponents and validation through scaled model exper- In order to optimize the locations for marine current turbine iments. Emphasis was placed on simple designs using conventional deployment, we apply mean-variance portfolio (MVP) theory to materials, and to the extent possible, commercial off-the-shelf create a portfolio consisting of multiple geographically diversified (COTS) components. Thus the cost and performance assumptions sites. MVP theory was developed by Markowitz [44] as a way to embedded in the RM4 design are deliberately conservative. devise an efficient financial portfolio consisting of different assets. Future innovations (e.g., advanced control strategies or advanced An efficient portfolio is the one with the least portfolio risk (typi- materials) could improve the assumed techno-economic cally modeled as total variance [45,46], or coefficient of variation performance. [47]) at a specified level of expected returns, such that one cannot The capital cost consists of pre-installation development, decrease the portfolio risk while increasing the expected return structural device components, power take-off, infrastructure, and level. project deployment costs, as shown in Supplementary Table G. MVP has been used to optimally site energy technologies, most Annual recurring costs include project operation and maintenance notably wind farms. Spreading wind farms over a wide geographic costs and recurring environment monitoring costs, as shown in area can decrease fluctuations in aggregate output and improve Supplementary Table H. Given the lack of commercial experience overall economic viability [45,46]. For example, Roques et al. [46] with this technology, we emphasize that substantial cost uncer- used historical wind production data from several European tainty exists, particularly given the need to operate in a harsh countries and applied MVP to optimally allocate wind farm capacity marine environment. in order to minimize the total variance associated with specific All capital costs incurred at the beginning of the project are electricity generation targets. multiplied by the capital charge rate (CCR) to calculate the annual MVP has also been applied to the repowering of existing wind payments required to pay off that investment over the assumed farms in Spain [48]. Santos-Alamillos et al. [48] find that portfolio project lifetime. The lifetime of the project is assumed to be 30 optimization can increase electricity production by 16e55% while years, based on the typical assumed lifetimes for marine energy reducing the hourly fluctuations in output by 12e31%. In Nova- projects. A discount rate of 10% is used to represent the cost of check and Johnson [49], different optimal wind portfolios were capital to an investor or utility. tested in a unit-commitment and dispatch model representing the Due to limited commercially available data for marine hydro- US Midwest power system in order to evaluate the value of reduced kinetic turbines, the capital costs for the structural device compo- variability to the system. generation smoothing was nents and power take-off are based on Neary et al. [10].We also investigated with MVP considering turbine failures and cor- subsequently compared the assumed capital cost with Verdant relation between aggregated wind power output and electricity Power's estimate for the Roosevelt Island Tidal Energy (RITE) demand [50]. Other works focus on using MVP to achieve an project [54] and found that the percentage difference between the optimal investment plan involving multiple energy resources [51] two estimates is only 0.2%. and to identify the best combined heat and power generation The cost of infrastructure consists of two major parts: the cost of 652 B. Li et al. / Energy 134 (2017) 649e658 the dedicated operations and maintenance (O&M) vessel and the 3. Results cost of the transmission system. The cost for the required electricity transmission is drawn from a similar project with undersea cables 3.1. Gulf Stream resource assessment tied to the North Carolina grid [55]. We assume the transmission system can be divided into two subsystems: a collection subsystem, As described in Section 2.1, we estimated annual capacity factors which transmits electricity from the turbines to the collection associated with marine turbines for all grid points within the study point, rated at a medium voltage of 33 kV; and a transmission domain (77 Wto74 W, 33 Nto36 N). Fig. 2aef shows the subsystem, which steps up the voltage to 132 kV and transmits the annual capacity factors and illustrate the significant spatiotemporal power received at the collection point to the onshore grid tie-in variability associated with hypothetical annual electricity produc- point [56]. The collection point is the hub that aggregates elec- tion. The sites with the highest capacity factors from 2009 to 2011 tricity from all the spur lines. To calculate transmission cable dis- are located in the southwestern quadrant whereas from 2012 to tances, the model assumes that the connection to the grid is located 2014 the highest capacity factors are found in the northeastern in Morehead City, NC, where existing transmission and distribution quadrant. Furthermore, the highest capacity factor in 2014 is over infrastructure exists [57]. Therefore, the total transmission cost is a 80%, but the same site has a capacity factor of only 50% in 2011. function of the total collection cable length, total transmission cable The average site-specific capacity factor over the six-year span distance, and number of installed units. See Supplementary Fig. D (2009e2014) is depicted in Fig. 2g. Note that the site with the and E for details on the transmission configuration. More details highest average six-year capacity factor is over 160 km away from on the infrastructure cost calculations can be found in Morehead City, the assumed grid tie-in point, and 230 km away Supplementary Note 3. from Cape Hatteras. The strongest currents with a capacity factor In this study, we calculate the LCOE using both single and greater than 40% are concentrated between the isobaths of 100 m multiple site configurations. In the single site configuration, we and 3000 m, since the stream flows over the upper continental calculate the LCOE associated with each individual grid cell and slope before it traverses the Atlantic towards Northern Europe. assume a dedicated transmission line to shore at Morehead City. In this layout, the total transmission distance equals the direct dis- 3.2. Correlation of current velocity and distance between sites tance between Morehead City and the grid cell, and for the gen- eration units installed in a single site, the total collection line The significant inter-annual variability in capacity factor at a consists of the spur lines for each separate 4 MW unit, which is an given location presents a serious economic challenge to potential average 1 km given the spacing distance between turbines. In the investors who may experience years with little or no electricity multisite configuration, grid cells are selected using portfolio production. One possible solution is to aggregate electricity gen- optimization and electricity output from each site is aggregated. In eration from multiple sites. this layout, we optimize the collection point location using a To explore the possibility of turbine site diversification, we Newton-Raphson iterative method such that the total cabling cost calculate the correlation in monthly electricity production from is minimized. 2009 to 2014 between all grid cell pairs in the study domain. Since The mooring design includes mooring cables, anchors, and land is included in the study domain, the number of site pairs as a buoyancy tanks, which are used to provide undersea support. function of distance is not uniform (Supplementary Fig. A). Fig. 3 Therefore, the total mooring costs are affected by both the number bins the correlation estimates by the nearest kilometer distance of units installed and the sea floor depth (h) at each installed site. between grid cell pairs. The upper and lower edges indicate the We followed Neary et al. [10] to calculate the total mooring cost, but maximum and minimum correlation, respectively, at the same modified the RM4 mooring design. In the RM4 design, the two- integer distance; all other samples at the same distance fall within point mooring system consists of tension and thrust lines that are the shaded region. secured to the seafloor. However, the mooring lines are attached to The average coefficients in Fig. 3 indicate that as the distance only one point on the turbine unit, which does not prevent the unit between two sites increases, the average coefficient of correlation from rotating about its vertical axis. Therefore, we include two approaches zero. In addition, the lowest coefficients of correlation additional tension lines and two additional thrust lines to balance occur at distances between 50 and 150 km, which corresponds to the turbine from lateral current forces [58]. As a result, our cost the approximate width of the Gulf Stream within the studied coefficient for mooring material is three times as expensive as the domain. If two sites are situated such that one site is in the Gulf estimate by Neary et al. [10]. Stream current and the other is not, their monthly energy outputs The costs associated with deployment include the cable shore will be more negatively correlated. Overall, the decreasing corre- landing, mooring and foundation system, cable installation, and lation as a function of distance implies that diversification of tur- device installation. Again, estimates drawn from Neary et al. [10] bine sites over a wide geographic area could reduce the total are used. We linearly scaled these cost estimates for project sizes variation in electricity production. ranging from 4 MW to 400 MW to obtain deployment cost per unit of installed capacity. 3.3. Portfolio optimization of generation sites Development costs mainly consist of siting and scoping, project design, engineering and management costs, and environmental Based on the US Department of Energy's (DOE) reference model compliance costs, such as permitting costs, National Environmental 4 (RM4) marine turbine design detailed in Neary et al. [10], each Policy Act (NEPA) compliance, and administrative costs. Logarith- turbine unit has an installed capacity of 4 MW, and a single mic regression is applied to fit the development cost estimates as a 2km 2 km grid cell can contain up to 16 MW of installed turbine function of capacity from Neary et al. [10]. capacity (See Supplementary Fig. B for more details.). To explore the O&M costs are associated with energy production and trans- optimal site locations associated with a larger installation, we mission on an ongoing basis. Annual fixed O&M costs are drawn conduct a portfolio optimization that requires a small but from Neary et al. [10]. It includes O&M for marine operations, manageable 80 MW of total installed capacity across no more than shore-based operations, replacement parts, and consumables. As 5 different locations. with deployment and development, a linear scaling is applied to As described in Section 2.2, the portfolio optimization model O&M costs. distributes installed capacity across different sites in order to B. Li et al. / Energy 134 (2017) 649e658 653

Fig. 2. Estimated capacity factor (aeg) and levelized cost of electricity (LCOE) (h) across the study domain. Crosses mark the locations with the highest annual capacity factors. Comparison of annual estimates indicates significant meanders and speed variations in the Gulf Stream. The triangle in (h) indicates the lowest LCOE. The 100 m, 1000 m, 2000 m and 3000 m bottom-depth contours (isobaths) are indicated by the black lines running southwest-to-northeast. The continental shelf is that portion of the ocean from the coastline to 100 m, and the continental slope extends seaward from the 100 m isobath. minimize the variance in total monthly electricity output at an efficient frontier when there is no integer constraint on the number exogenously specified capacity factor target. In order to make the of installed generating units. The Stage 2 results represent the formulation computationally tractable, the portfolio optimization is modified efficient frontier when the integer constraint on the performed in two stages. Fig. 4 presents the tradeoff between ca- number of generating units is placed on the candidate sites chosen pacity factor and variance. The Stage 1 results represent the in Stage 1. 654 B. Li et al. / Energy 134 (2017) 649e658

cell left in the portfolio; the inclusion of any other grid cells fails to meet the target capacity factor. Thus, as the target capacity factor is increased, the potential reduction in covariance through site diversification is reduced. As expected, the gap between the Stage 1 and 2 frontiers in Fig. 4 implies that the addition of integer con- straints slightly worsens the optimization results, since the port- folio variance increases. Furthermore, the addition of integer constraints in Stage 2 affect the achievable capacity factor, hence the misalignment between the Stage 1 and 2 capacity factor targets. Fig. 5 shows the optimal site locations from portfolios with different target capacity factors. The selected sites range from the 100 m and 2500 m isobaths due to the bathymetry constraint based on limits to anchoring depth. The number of selected sites in each Stage 1 portfolio is less than 20, even though there are over 4000 candidate sites. In addition, most of the selected sites are clustered around the site with the highest six-year average capacity factor, represented by the cross. When the target capacity factor is low, the selected sites tend to spread out over a larger geographic area to take advantage of weaker correlations in output. Fig. 3. Correlation in monthly electricity production versus distance for each pair of grid cells in the study domain. The correlation estimates are binned by distance to the nearest kilometer. The minimum, average, and maximum correlation coefficient at 3.4. Levelized cost study each distance are shown as lines; all other site pairs fall within the gray region. It is possible to formulate the portfolio optimization problem with a constraint on LCOE rather than capacity factor. However, For comparison, the dots represent the minimum variance at a such a formulation would lead to a more complex non-linear model given capacity factor target that can be obtained when only one due to the interaction between the capacity allocated to a specific grid cell is selected. The cross at the top of Fig. 4 marks the site and the energy production from the turbines within the site, maximum 6-year average capacity factor among all the sites in the which in turn depends on the allocated capacity. Thus, while the fi domain. The results illustrate that it is possible to signi cantly portfolio study indicates the tradeoff between variability and total reduce the variance in energy output at a given capacity factor by output, it does not take cost into account. creating a portfolio of geographically dispersed sites rather than Fig. 2h presents the LCOE from individual sites and indicates relying on a single site. For example, among all individual sites with that at the center of the Gulf Stream, the lowest LCOE is slightly capacity factor equal to 40%, the minimum variance is approxi- 2 above 400 $/MWh. Sites with the lowest LCOEs are located near the mately 60,000 (MWh/month) , while the best portfolio can reduce center of the Gulf Stream, which is consistent with Fig. 2g, since a the total variance approximately 20 times to 3000 (MWh/month)2. higher site-specific capacity factor implies a lower LCOE. Interest- The variance reductions through portfolio optimization, which ingly, the site with the highest six-year average capacity factor is are represented by the horizontal distances between the efficient not the same as that with the lowest six-year average LCOE, as frontier and the solid dots on Fig. 4, decrease as the required target illustrated in Fig. 2h. The site with the lowest LCOE, indicated by a capacity factor increases. When the target capacity factor is equal to triangle, is closer to Morehead City, the assumed grid tie-in point, the maximum capacity factor across all sites, there is only one grid than the site with the highest six-year average capacity factor, as marked with a cross. The distance between the two sites is approximately 35 km. This represents the tradeoff between energy quality and transmission cost: it is more cost-effective to select a site with marginally lower resource quality but a shorter trans- mission distance. The results depicted in Fig. 2 provide a useful visualization of the resource quality and LCOE over a continuous domain. To study the LCOE as a function of the cumulative amount of electricity gener- ation from the Gulf Stream, supply curves for the years 2009e2014 are shown in Fig. 6. These curves represent the marginal cost to produce the next increment of electricity. As more electricity is generated, the cost to extract it becomes more expensive as loca- tions with declining resource quality must be utilized. For simplicity, we assume that the addition of each new site requires dedicated transmission lines to Morehead City. In addition, we account for array losses by applying a scaling factor that reduces the output at each site by approximately 53%.1While a more accurate accounting of array losses would require modeling that accounts for the incremental array losses as new capacity is deployed, Fig. 6 nonetheless illustrates how inter-annual variability in the Gulf Stream resource affects LCOE. The LCOE at a given production level Fig. 4. Results from the portfolio optimization. Stage 1 results represent the optimal portfolio without an integer constraint on the number of turbine units, while Stage 2 results use the candidate sites selected from Stage 1 and include the integer constraint. The scattered dots to the right indicate the minimum variance among individual grid 1 This estimate is drawn from Yang et al. [7] by comparing scenarios with zero cells with the same capacity factor targets rounded to the nearest percent. drag coefficient (i.e., no array losses) and a uniform drag coefficient. B. Li et al. / Energy 134 (2017) 649e658 655

Fig. 5. Selected sites within the optimal portfolios at different minimum capacity factor targets. The filled circles on each figure indicate the location of installed capacity in Stage 1 solutions, while the open circles indicate installed capacity in Stage 2 solutions. For reference, the cross indicates the location of the site with the maximum six-year average capacity factor. The background color shading represents the six-year average capacity factors (CF) from 2009 to 2014, and the inset provides an expanded view of the selected sites near 33 N and 77 W. can vary by more than 300 $/MWh from one year to the next. These However, the LCOE is not monotonically decreasing with results suggest that inter-annual variability in Gulf Stream intensity increasing capacity factor: the LCOE increases when the capacity can have a significant impact on year-to-year costs and revenue. factor increases from 46% to 47%, from 49% to 50% and from 52% to While we did not directly constrain the LCOE in the portfolio 53%. These variations are due to transmission cost, and to a lesser optimization, Fig. 7a shows the LCOE calculated ex post as a function extent, mooring cost. Among all cost components, the power take- of the target capacity factor. Since we include project economies of off and transmission infrastructure are the two principal cost scale based on Neary et al. [10], the portfolio-based LCOE with drivers. Each time the target capacity factor increases, the model installed capacity of 80 MW is lower than that of a 16 MW single returns a new portfolio that includes a different set of sites with the site; the entire LCOE profile in the former case is below 400 $/MWh. same total installed capacity. Given the fixed installed capacity, the As expected, the LCOE is inversely correlated with capacity factor device structural components cost, power take-off cost, develop- since higher capacity factors represent higher annual electricity ment cost and deployment cost remain the same, but the infra- production. structure cost will be affected by the transmission distance (see Supplementary Note 3). In addition, changing the site selection also affects the assumed depths, which in turn affect mooring cost. In some cases, the incremental increase in infrastructure and mooring cost outweighs the incremental increase in electricity production, and the LCOE increases with the capacity factor. Thus, while an increasing capacity factor target increases the energy yield, it does not guarantee a lower LCOE. Fig. 7b compares the cost breakdown of the turbine arrays in both the single site and optimal portfolios by showing the per- centage shares of each component contributing to the total annu- alized cost. The sample set associated with the single site case covers the whole sub-domain, while the optimal portfolio case only contains 20 optimal portfolios, representing the 20 different ca- pacity factor targets (from 0.40 to 0.59). The wider spread in the single site layout indicates a broader range of transmission dis- tances and mooring depths associated with the larger domain. By contrast, the smaller ranges in Fig. 7b associated with the optimal portfolios reflect the much smaller sample size as well as the clustering of selected sites: most sites are grouped around the location with the highest average capacity factor, therefore the transmission distances are similar. The results indicate that power fi Fig. 6. Annual supply curves from 2009 to 2014. Signi cant inter-annual variability in take-off components and transmission infrastructure are the two LCOE at a given production level can be observed. 656 B. Li et al. / Energy 134 (2017) 649e658

Fig. 7. LCOE analysis for the portfolios from the MVP model. (a) LCOE calculated ex post as a function of the capacity factor target in the portfolio optimization. (b) Box plot showing the share of LCOE attributable to different cost components in both the single site and portfolio cases, ordered from highest to lowest share in the portfolio case. The edges of each box represent the 25th and 75th percentiles, and the whiskers extend to the maximum and minimum values. leading cost drivers. In addition, when the installed capacity in- position increases northeastward from the “Charleston bump” and creases from 16 MW in the single site to 80 MW in the portfolio, the then decreases on towards Cape Hatteras due to the steepening of percentage shares of infrastructure, deployment and development the continental slope approaching Cape Hatteras [19,23,24,27,62]. decrease due to the inclusion of project economies of scale for these In addition, the envelope of the Gulf Stream meandering down- components, which in turn lead to the increase of the percentage stream of Cape Hatteras broadens to 200e300 km or more shares of device structural components and power take-off. [25,60,61], greater than its own width of about 100 km, compared In the portfolio analysis, the estimated LCOE drops from 350 to the maximum lateral movement of around 40 km [19] from $/MWh to 230 $/MWh when the capacity factor increases from 40% Charleston to Cape Hatteras. In summary, both the oceanographic to 59%. For comparison, Jenne et al. [36] estimate an LCOE of study and the portfolio optimization indicate that the region con- approximately 200 $/MWh for an 80 MW installation in the Florida taining the Gulf Stream currents approximately 200 km southwest Straits. The reason for the higher LCOE in the North Carolina case is of Cape Hatteras is the most cost-effective location to deploy tur- twofold: capacity factors in the Florida Current are consistently bines along the North Carolina coastline. around 70%, which is higher than even the best site in this study; Several caveats should be noted. First, there are significant un- and the transmission distances in North Carolina are significantly certainties associated with cost given the lack of commercial greater than in the Florida Straits. The average transmission dis- experience with this technology. Second, while the 6-year MABSAB tance from the collection point to Morehead City is around ocean model hindcast dataset enables a critical examination of 160e180 km, compared with 30 km in the Florida Straits. inter-annual variability in Gulf Stream energy resources, a longer record would help to better characterize the economic effects of 4. Discussion meanders. Third, in this study, the LCOE associated with the optimal portfolios are calculated ex post. While Fig. 7a indicates that The resource quality associated with Gulf Stream current energy capacity factor is a reasonable proxy for LCOE, changes in the off the North Carolina coast is highly variable. Fig. 2 shows that transmission and mooring costs can increase the LCOE at higher model-computed capacity factors exhibit significant spatiotem- capacity factor targets. poral variability due to path meanders and speed variations in the A revised optimization model that makes LCOE rather than ca- Gulf Stream. Around 35 North latitude, the average location of the pacity factor the driving constraint would be preferable, but would shoreward edge of the Gulf Stream moves from the 3000 m isobath result in a more complex non-linear model. The class of mixed- in 2010 to between the 2000 and 3000 m isobaths in 2012, while integer nonlinear optimization problems is one of the hardest to the Gulf Stream position around 33 North remains fixed. This solve in the optimization literature [63], particularly when it is a observation is consistent with previous studies [25,27,59], where constrained non-convex optimization model. According to Mansini the Gulf Stream's path is found to have similar inter-annual et al. [63], there are no algorithms for the exact solution of non- variations. convex nonlinear programming problems in which the feasible The optimized portfolio of generation sites, which aggregates region is a mixed-integer set. This raises concerns about reaching a electricity production from geographically diversified turbine units, local instead of a global optimal [64] and requires exhaustive can significantly reduce the variability in electricity generation and computational time or the use of a metaheuristic technique [65] to improve the economic prospects of the technology. Similar to wind find an approximate solution when solving the model. farms, site diversification can reduce the need for back-up reserves. Gulf Stream energy off the North Carolina coast will not be a Fig. 5 indicates that as the target capacity factor increases, the viable option without significant cost reductions: our model shows selected sites cluster around the southwestern quadrant of the that the optimized portfolios have LCOEs ranging from 230 to 350 study domain where the site with the highest six-year $/MWh. By comparison, Jenne et al. [36] estimated an LCOE of 200 average capacity factor is located. Another advantage of deploying $/MWh for ocean current energy in the Florida Straits, a tier-one turbine arrays in this region is that the lateral amplitude of the Gulf site located 30 km east of Fort Lauderdale. Both estimates are Stream meander is near a minimum within the domain still far higher than baseload sources such as , steam and nat- [19,23e25,27,59e61]. For that portion of the Gulf Stream upstream ural gas combined cycle, which have LCOEs ranging from 70 to 100 of Cape Hatteras, the standard deviation of the surface front $/MWh [66]. It is also not competitive with commercially mature B. Li et al. / Energy 134 (2017) 649e658 657 renewables such as solar photovoltaics and wind, which can be as stream active mooring: Part I. Renew Energy 2017;109:144e54. http:// low as 70 $/MWh [66]. Nonetheless, a range of technologies must dx.doi.org/10.1016/j.renene.2017.02.065. [15] Marais E, Chowdhury S, Chowdhury SP. 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